In this Course you learn k-Nearest Neighbors & Naive Bayes Classification Methods. In pattern recognition, the k-nearest neighbors algorithm (k-NN) is a non-parametric method used for classification and regression. The k-NN algorithm is among the simplest of all machine learning algorithms. For classification, a useful technique can be to assign weight to the contributions of the neighbors, so that the nearer neighbors contribute more to the average than the more distant ones. The neighbors are taken from a set of objects for which the class (for k-NN classification).

We introduce a generalized dual decomposition bound for computing the maximum expected utility of influence diagrams based on the dual decomposition method generalized to $L^p$ space.  The main goal is to devise an approximation scheme free from translations required by existing variational approaches while exploiting the local structure of sum of utility functions as well as the conditional independence of probability functions.  In this work, the generalized dual decomposition method is applied to the algebraic framework called valuation algebra for influence diagrams which handles probability and expected utility as a pair. The proposed approach allows a sequential decision problem to be decomposed as a collection of sub-decision problems of bounded complexity and the upper bound of maximum expected utility to be computed by combining the local expected utilities. Thus, it has a flexible control of space and time complexity for computing the bound.  In addition, the upper bounds can be further minimized by reparameterizing the utility functions. Since the global objective function for the minimization is nonconvex, we present a gradient-based local search algorithm in which the outer loop controls the randomization of the initial configurations and the inner loop tightens the upper-bound based on block coordinate descent with gradients perturbed by a random noise. The experimental evaluation demonstrates highlights of the proposed approach on finite horizon MDP/POMDP instances.

Structure learning is a fundamental and challenging issue in dealing with Bayesian networks. In this paper we introduce a two-step clustering-based strategy, which can automatically generate prior information from data in order to further improve the accuracy and time efficiency of state-of-the-art algorithms in Bayesian network structure learning. Our clustering-based strategy is composed of two steps. In the first step, we divide the potential nodes into several groups via clustering analysis and apply Bayesian network structure learning to obtain some pre-existing arcs within each cluster. In the second step, with all the within-cluster arcs being well preserved, we learn the between-cluster structure of the given network. Experimental results on benchmark data sets show that a wide range of structure learning algorithms benefit from the proposed clustering-based strategy in terms of both accuracy and efficiency.

This paper addresses the general problem of accurate identification of oil reservoirs. Recent improvements in well or borehole logging technology have resulted in an explosive amount of data available for processing. The traditional methods of analysis of the logs characteristics by experts require significant amount of time and money and is no longer practicable. In this paper, we use the semi-supervised learning to solve the problem of ever-increasing amount of unlabelled data available for interpretation. The experts are needed to label only a small amount of the log data. The neural network classifier is first trained with the initial labelled data. Next, batches of unlabelled data are being classified and the samples with the very high class probabilities are being used in the next training session, bootstrapping the classifier. The process of training, classifying, enhancing the labelled data is repeated iteratively until the stopping criteria are met, that is, no more high probability samples are found. We make an empirical study on the well data from Jianghan oil field and test the performance of the neural network semi-supervised classifier. We compare this method with other classifiers. The comparison results show that our neural network semi-supervised classifier is superior to other classification methods.

Learning latent variable models with stochastic variational inference is challenging when the approximate posterior is far from the true posterior, due to high variance in the gradient estimates. We propose a novel rejection sampling step that discards samples from the variational posterior which are assigned low likelihoods by the model. Our approach provides an arbitrarily accurate approximation of the true posterior at the expense of extra computation. Using a new gradient estimator for the resulting unnormalized proposal distribution, we achieve average improvements of 3.71 nats and 0.21 nats over state-of-the-art single-sample and multi-sample alternatives respectively for estimating marginal log-likelihoods using sigmoid belief networks on the MNIST dataset.

We present an end-to-end trained memory system that quickly adapts to new data and generates samples like them. Inspired by Kanerva's sparse distributed memory, it has a robust distributed reading and writing mechanism. The memory is analytically tractable, which enables optimal on-line compression via a Bayesian update-rule. We formulate it as a hierarchical conditional generative model, where memory provides a rich data-dependent prior distribution. Consequently, the top-down memory and bottom-up perception are combined to produce the code representing an observation. Empirically, we demonstrate that the adaptive memory significantly improves generative models trained on both the Omniglot and CIFAR datasets. Compared with the Differentiable Neural Computer (DNC) and its variants, our memory model has greater capacity and is significantly easier to train.

All reinforcement learning algorithms must handle the trade-off between exploration and exploitation. Many state-of-the-art deep reinforcement learning methods use noise in the action selection, such as Gaussian noise in policy gradient methods or $\epsilon$-greedy in Q-learning. While these methods are appealing due to their simplicity, they do not explore the state space in a methodical manner. We present an approach that uses a model to derive reward bonuses as a means of intrinsic motivation to improve model-free reinforcement learning. A key insight of our approach is that this dynamics model can be learned in the latent feature space of a value function, representing the dynamics of the agent and the environment. This method is both theoretically grounded and computationally advantageous, permitting the efficient use of Bayesian information-theoretic methods in high-dimensional state spaces. We evaluate our method on several continuous control tasks, focusing on improving exploration.

Identifying anomalous patterns in real-world data is essential for understanding where, when, and how systems deviate from their expected dynamics. Yet methods that separately consider the anomalousness of each individual data point have low detection power for subtle, emerging irregularities. Additionally, recent detection techniques based on subset scanning make strong independence assumptions and suffer degraded performance in correlated data. We introduce methods for identifying anomalous patterns in non-iid data by combining Gaussian processes with novel log-likelihood ratio statistic and subset scanning techniques. Our approaches are powerful, interpretable, and can integrate information across multiple data streams. We illustrate their performance on numeric simulations and three open source spatiotemporal datasets of opioid overdose deaths, 311 calls, and storm reports.

We consider the problem of estimating the transition rate matrix of a continuous-time Markov chain from a finite-duration realisation of this process. We approach this problem in an imprecise probabilistic framework, using a set of prior distributions on the unknown transition rate matrix. The resulting estimator is a set of transition rate matrices that, for reasons of conjugacy, is easy to find. To determine the hyperparameters for our set of priors, we reconsider the problem in discrete time, where we can use the well-known Imprecise Dirichlet Model. In particular, we show how the limit of the resulting discrete-time estimators is a continuous-time estimator. It corresponds to a specific choice of hyperparameters and has an exceptionally simple closed-form expression.

Logistic Regression is one of the most powerful classification methods within machine learning and can be used for a wide variety of tasks. Think of pre-policing or predictive analytics in health; it can be used to aid tuberculosis patients, aid breast cancer diagnosis, etc. Think of modeling urban growth, analysing mortgage pre-payments and defaults, forecasting the direction and strength of stock market movement, and even predicting sport outcomes. Reading all of this, the theory[1] of Maximum Entropy Classification might look difficult. In my experience, the average Developer does not believe they can design a proper Maximum Entropy / Logistic Regression Classifier from scratch. I strongly disagree: not only is the mathematics behind is relatively simple, it can also be implemented with a few lines of code.